Singular Fields Study Around The Tip Of Multi-material Wedges And Junctions Based On Non-confirming Finite Element FE Eigenanalysis Method

In this paper a new non-conforming finite element FE eigenanalysis method based on displacement is developed to study the singular displacement and stress fields around a 2D or 3D wedge tip. There are several points different from the existing finite element eigenanalysis methods for asymptotic fields near the crack tip: 1) The standpoint to derive formula is different. 2) The form of the element is non-conforming element. 3) The singular transformation technique is not used in the assumption of displacement fields around the wedge tip. According to types of multi-material combinations and study interests, this paper presents the singular fields of four kinds of problems: 1) isotropic problems under inplane stress;2) anisotropic problems under inplane stress;3) antiplane problems of isotropic and anisotropic multi-materials;4) three-dimensional anisotropic multi-material junctions problems. For each problem, this paper examines the singular fields of one-material, two-material and three-material wedges and junctions, evaluates their singularities and the angular variations of displacement and stress fields separately. The singularities (eigenvalues) and eigenvectors are obtained by solving the non-conforming FE characteristic equations, the angular variations of displacement are obtained by the multiplication of interpolation functions matrix and eigenvectors, and the angular variations of stresses are obtained by the multiplication of stress matrices and eigenvectors. All calculations show that the present method needs fewer elements, and yields more accurate results than available methods. According to the values of singularities and the qualities of the angular variations of displacements and stresses, we know the states of singular fields about multi-material combinations, which can help us to estimate damage degree or stand and fall of multi-material junctions.